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# If a and b are two numbers such that a*b = 10, is a an integer ?

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Current Student
Joined: 12 Aug 2015
Posts: 2567
Schools: Boston U '20 (M)
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If a and b are two numbers such that a*b = 10, is a an integer ?  [#permalink]

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Updated on: 19 Jul 2016, 04:28
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75% (hard)

Question Stats:

54% (02:00) correct 46% (01:24) wrong based on 72 sessions

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If a and b are two numbers such that a*b = 10, is a an integer ?

(1) 2a is an integer
(2) b is a not an integer

Note => i found this on a random site ..! I think its answer is wrong Anybody with me?

_________________

Originally posted by stonecold on 19 Jul 2016, 02:51.
Last edited by Bunuel on 19 Jul 2016, 04:28, edited 2 times in total.
Edited the OA.
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Joined: 02 Sep 2009
Posts: 58449
Re: If a and b are two numbers such that a*b = 10, is a an integer ?  [#permalink]

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19 Jul 2016, 04:27
2
1
stonecold wrote:
If a and b are two numbers such that a*b = 10, is a an integer ?

(1) 2a is an integer
(2) b is a not an integer

Note => i found this on a random site ..! I think its answer is wrong Anybody with me?

The answer is neither B nor C, it's E.

Consider the following cases:
a = 20 and b = 1/2 (2a is an integer and b is a not an integer);
a = 3/2 and b = 20/3 (2a is an integer and b is a not an integer).

Hope it helps.
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Location: India
Re: If a and b are two numbers such that a*b = 10, is a an integer ?  [#permalink]

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19 Jul 2016, 03:25
1
If B = 35/3 and A = 6/7 we still get AB= 10 ...
Is B really the OA?
Retired Moderator
Joined: 26 Nov 2012
Posts: 569
Re: If a and b are two numbers such that a*b = 10, is a an integer ?  [#permalink]

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19 Jul 2016, 03:30
1
stonecold wrote:
msk0657 wrote:
stonecold wrote:
If a and b are two numbers such that a*b = 10; Is a an integer ?
A-) 2a is an integer
B-) b is a not an integer

Given that a and b are two numbers such that a*b = 10 and asking us to find the if a is integer ?

Stat 1: 2a = integer.

if a = 1 (integer) then 2a is 2 - integer.
if a = 1/2 (non-integer) then 2a is 1 - integer... we get different answers...Insufficient.

Stat 2: b is not an integer

then out of ab = 10 , for ex : if b is 1/10 then a has to be 100 . Then in case b is rational then a has to be integer if at all if we want to get ab = 10......Sufficient.

Hence option B is correct.

I am sure sure i get your solution..
then the test case approach would have been longer one
i think the logic may here be => "If the product of two integers is an integer then one of them must be an integer"
Hence B .

The question didn't about 19..ok if it is 19 ... then take a or b as 38 or a or b as 1/2...even then it works quickly... Then we have two cases for a itself i.e 38 or 1/2.

"If the product of two integers is an integer then one of them must be an integer" - You are correct...if it is in the question, if they ask about which one is integer then you have to try the test case approach itself...
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Re: If a and b are two numbers such that a*b = 10, is a an integer ?  [#permalink]

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19 Jul 2016, 06:23
1
got it as E

i hope u guys concur that either 1 or 2 is not suff

i will take both cases:

a=3/2 b=20/3(obeys 1 and 2)

or

a=3 b=10/3(obeys 1 and 2)

Retired Moderator
Joined: 26 Nov 2012
Posts: 569
Re: If a and b are two numbers such that a*b = 10, is a an integer ?  [#permalink]

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19 Jul 2016, 03:11
stonecold wrote:
If a and b are two numbers such that a*b = 10; Is a an integer ?
A-) 2a is an integer
B-) b is a not an integer

Given that a and b are two numbers such that a*b = 10 and asking us to find the if a is integer ?

Stat 1: 2a = integer.

if a = 1 (integer) then 2a is 2 - integer.
if a = 1/2 (non-integer) then 2a is 1 - integer... we get different answers...Insufficient.

Stat 2: b is not an integer

then out of ab = 10 , for ex : if b is 1/10 then a has to be 100 . Then in case b is rational then a has to be integer ( a = 10 * b )if at all if we want to get ab = 10......Sufficient.

Hence option B is correct.
Current Student
Joined: 12 Aug 2015
Posts: 2567
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If a and b are two numbers such that a*b = 10, is a an integer ?  [#permalink]

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Updated on: 19 Jul 2016, 03:43
msk0657 wrote:
stonecold wrote:
If a and b are two numbers such that a*b = 10; Is a an integer ?
A-) 2a is an integer
B-) b is a not an integer

Given that a and b are two numbers such that a*b = 10 and asking us to find the if a is integer ?

Stat 1: 2a = integer.

if a = 1 (integer) then 2a is 2 - integer.
if a = 1/2 (non-integer) then 2a is 1 - integer... we get different answers...Insufficient.

Stat 2: b is not an integer

then out of ab = 10 , for ex : if b is 1/10 then a has to be 100 . Then in case b is rational then a has to be integer if at all if we want to get ab = 10......Sufficient.

Hence option B is correct.

I am sure sure i get your solution..
then the test case approach would have been longer one
i think the logic may here be => "If the product of two integers is an integer then one of them must be an integer"
_________________

Originally posted by stonecold on 19 Jul 2016, 03:23.
Last edited by stonecold on 19 Jul 2016, 03:43, edited 1 time in total.
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Joined: 26 Nov 2012
Posts: 569
Re: If a and b are two numbers such that a*b = 10, is a an integer ?  [#permalink]

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19 Jul 2016, 03:39
HMC wrote:
If B = 35/3 and A = 6/7 we still get AB= 10 ...
Is B really the OA?

You are correct B = 35/3 and A = 6/7 then AB is 10.

Then as per Stat 2 : it is mentioned that b is not integer . If you take rational, mixed numbers then can write in fraction form

We have no idea about A and we can't take it A as integer or non integer number, from stat 2 we are going to find the value from the stem.
Current Student
Joined: 12 Aug 2015
Posts: 2567
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If a and b are two numbers such that a*b = 10, is a an integer ?  [#permalink]

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19 Jul 2016, 03:45
See msk0657 and HMC this isnt a official question..!
I found it on the internet
It mentioned B being correct...!!
But if it is really asked on the gmat my money is on option C.
CC- Bunuel
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Re: If a and b are two numbers such that a*b = 10, is a an integer ?  [#permalink]

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19 Jul 2016, 03:50
I still think it should be C ..!!
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Re: If a and b are two numbers such that a*b = 10, is a an integer ?  [#permalink]

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27 Jul 2017, 10:31
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Re: If a and b are two numbers such that a*b = 10, is a an integer ?   [#permalink] 27 Jul 2017, 10:31
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